1/2+1/6+1/12+1\20+1/30+1/42+.+1/9900=?

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1/2+1/6+1/12+1\20+1/30+1/42+.+1/9900=?

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/99-1/100)
=1-1/100
=99/100